1. satisfaz a 2. actua como métrica avaliadora

English translation: >> see below <<

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No. 1 is placed within an 'equation' which goes something like this
M= (U subset symbol V) satisfaz a eq. 3.80
How can I render 'satisfaz a'?
No. 2 ..acts as ?
Finally, No 3 is 'representation in 'escala de cinzentos', the corresponding 'grau de cinzento' How can I translate cinzento?

Explanation:1) "satisfaz a" = "satisfies," as in "M = (U -subset- V) satisfies equation 3.80."
The English phrase "to satisfy an equation" is a very common one in maths, and simply means that a particular relationship meets the conditions indicated in a particular equation.

2) "actua como métrica avaliadora" = "acts as evaluative metric"; however, I'd suggest the less literal "serves as an evaluative metric." ("Metric" here is a noun, and is synonymous with "benchmark" or, more colloquially, "yardstick.")

3a) "representation in 'escala de cinzentos'" = "shown in [the form of a] gray-scale [illustration]"

3b) "grau de cinzento" = "gray level"
The term "gray scale," which comes from photography and printing, refers to a picture or illustration that consists of multiple different shades of gray, as opposed to simply black and white. Each of the shades of gray in a gray-scale illustration is referred to as a "gray level," or simply "level." You may have heard scanners or fax machines described as "16-gray-level" or "32-gray-level" devices. (NOTE: The number of gray levels almost always increases in powers of 2; that is, from 4 to 8 to 16 to 32 to 64 to 128 to 256, and so on.)

Explanation:1) "satisfaz a" = "satisfies," as in "M = (U -subset- V) satisfies equation 3.80."
The English phrase "to satisfy an equation" is a very common one in maths, and simply means that a particular relationship meets the conditions indicated in a particular equation.

2) "actua como métrica avaliadora" = "acts as evaluative metric"; however, I'd suggest the less literal "serves as an evaluative metric." ("Metric" here is a noun, and is synonymous with "benchmark" or, more colloquially, "yardstick.")

3a) "representation in 'escala de cinzentos'" = "shown in [the form of a] gray-scale [illustration]"

3b) "grau de cinzento" = "gray level"
The term "gray scale," which comes from photography and printing, refers to a picture or illustration that consists of multiple different shades of gray, as opposed to simply black and white. Each of the shades of gray in a gray-scale illustration is referred to as a "gray level," or simply "level." You may have heard scanners or fax machines described as "16-gray-level" or "32-gray-level" devices. (NOTE: The number of gray levels almost always increases in powers of 2; that is, from 4 to 8 to 16 to 32 to 64 to 128 to 256, and so on.)